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5.Work, Energy, Power and Collision
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A body of mass $m$ hangs at one end of a string of length $l$, the other end of which is fixed. It is given a horizontal velocity so that the string would just reach where it makes an angle of $60^o$ with the vertical. The tension in the string at mean position is
A$2\,mg$
B$mg$
C$3\,mg$
D$\sqrt3\, mg$
Solution
When body is released from the position $p$ (inclined at angle $\theta$ from vertical) then velocity at mean position
$\mathrm{v}=\sqrt{2 \mathrm{g}\ell (1-\cos \theta)}$
Tension at the lowest point $=\mathrm{mg}+\frac{\mathrm{mv}^{2}}{\ell}$
$=m g+\frac{m}{\ell}[2 g \ell(1-\cos 60)]=m g+m g=2 m g$
$\mathrm{v}=\sqrt{2 \mathrm{g}\ell (1-\cos \theta)}$
Tension at the lowest point $=\mathrm{mg}+\frac{\mathrm{mv}^{2}}{\ell}$
$=m g+\frac{m}{\ell}[2 g \ell(1-\cos 60)]=m g+m g=2 m g$
Standard 11
Physics
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